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Search: id:A072873
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| A072873 |
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Numbers n such that sum( e(i)/p(i) ) is an integer, where the prime factorization of n is prod ( p(i)^e(i) ). |
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5
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| 1, 4, 16, 27, 64, 108, 256, 432, 729, 1024, 1728, 2916, 3125, 4096, 6912, 11664, 12500, 16384, 19683, 27648, 46656, 50000, 65536, 78732, 84375, 110592, 186624, 200000, 262144, 314928, 337500, 442368, 531441, 746496, 800000, 823543
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OFFSET
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1,2
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COMMENT
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Also, numbers n such that n divides n', the arithmetic derivative of n. As shown by Ufnarovski and Ahlander, all terms in this sequence have the form prod_{k=1..r} (pk^pk)^ek, where the pk are primes. The quotient n'/n equals sum_{k=1..r} ek. - T. D. Noe (noe(AT)sspectra.com), Jan 04 2006
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REFERENCES
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See A003415.
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EXAMPLE
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108 is in the sequence because 108 = 2^2*3^3 and 2/2+3/3 = 2 is an integer
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CROSSREFS
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Sequence in context: A046346 A134330 A097764 this_sequence A072653 A008478 A137231
Adjacent sequences: A072870 A072871 A072872 this_sequence A072874 A072875 A072876
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 28 2002
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Jan 04 2006
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